As was already explained before, a perpetuity is a form of annuity that has an endless number of periodic payments. Usually, investments such as preferred stocks and annuities are not expected to appreciate, and therefore they are valued for their ongoing dividends/payments. In principle, these ongoing periodic payments are touted as perpetuity. Nevertheless, as time goes by the interest rate may change, and it may affect the value of the perpetual investment.
The formula that is used to calculate the yield on perpetuity is the bond’s periodic payment divided by the present value of the perpetuity.
Perpetuity Yield = Payment/PV
PV = Present Value of the perpetual bond that is determined by discounting the identical infinite cash flows with the discounting rate that amounts to a limited value.
Therefore,
PV of Perpetuity = ICF/r
where,
ICF - the identical cash flows
r - the interest rate or the discounting rate
or
PV of Perpetuity = ICF/(r – g)
where,
g – perpetuity growth rate (in case the perpetuity grows by a constant growth rate)
For instance, let us assume that a perpetual bond will pay $1000 per annum forever, the required rate of return is 10%. Then, the PV of perpetuity will be:
$1000/0.1 = $10000
Further, using the formula for calculating the perpetuity yield, we will arrive at:
Perpetuity Yield = $1000/$10000 = 0.10, or 10%.
It should be remembered that perpetuity formulas tend to be conceptual and not set in stone. An investor will want a higher rate of return for a riskier investment. If the interest rates change over time, the discount rates will also have to be adjusted in the formula.
Stay with us, and in our next post, we will touch upon the concept of convertible bonds.